Question

Identifying Lengths of the Sides of a Right Triangle.

Which are the side lengths of a right triangle? Check all that apply.
3, 14, and square root 205
6,11, and square root 158
19, 180, and 181
3, 19, and square root 380
2, 9, and square root 85

Answer 1

not sure. I got the numbers right, but right angle no

Explanation:

Answer 2

The side lengths of a right triangle among the given options are

1. 3, 14, and square root 205
2. 2, 9, and square root 85

Solution:

Let us assume that the three sides of a right triangle are a, b and c

So as per Pythagoras theorem, we know,

`a^(2)+b^(2)=c^(2)`

Here for 3, 14, and square root 205,

`(√(205))^(2)=205`

`3^(2)+14^(2)=9+196=205`

So this satisfies the right triangle

For 6,11, and square root 158

`(√(158))^(2)=158`

`6^(2)+11^(2)=157`

So this do not satisfy the right triangle

For 19, 180, and 181

`(√(181))^(2)=181`

`19^(2)+180^(2)=32400`

So this do not satisfy the right triangle

Again for 3, 19, and square root 380

`(√(380))^(2)=380`

`3^(2)+19^(2)=9+361=370`

So this do not satisfy the right triangle

For 2, 9, and square root 85

`(√(85))^(2)=85`

`2^(2)+9^(2)=85`

So, this satisfies the right triangle .